Part II - Data Processing & Analysis

This section is about processing raw population data and sample data, and taking a first look at finding the probability of producing an observed set of results based on estimated or computer population parameters.

5.The population data for all 12,515 of Wishbone's previous customers.The data shows a value of 1 if the customer placed an order in the last month, and a 0 if the customer did not place an order in the last month. The total number of orders placed or (1) is 10,343 and the total number of orders not placed or (0) is 2,172.

a. What type of distribution would describe this data? Be sure to check all the requirements!

b. Count the number of values of 1 and divide by the total number of values to find the population proportion,p, of customers who placed an order in the last month.

c. Use the formula for the appropriate distribution to calculate the standard deviation of the population.

Sample 1 was selected using systematic sampling of every 120^th customer; Sample 2 was taken using stratified sampling of new customers vs previous customers; Sample 3 was taken using stratified sampling of high value customers (>$20) vs low value customers (<$20); Sample 4 was taken using cluster sampling; and Sample 5 is a simple random sample.

6. For each Sample, count the number of customers who did place an order in the past month and divide by the sample size of 100 to find , the sample proportion.

a. Sample 1:

b. Sample 2:

c. Sample 3:

d. Sample 4:

e. Sample 5:

7. Now, use the 5 sample proportions you found in the previous problem as your data; you may either enter them in a new dataset or you may find it easier to simply enter the values in L1 on your calculator and compute 1-Var Stats.

a. Calculate the mean value of the sample proportions.

b. Calculate the population standard deviation, , for the sample proportions. How does this compare to the standard deviation of the original population?

8. Use the value ofp computed in problem 5 as the population parameterp.

a. What is the mean value of the sampling distribution, ?

b. Calculate the value of the standard error of the sampling distributions with a sample size of , that is, . How does this compare to the standard deviation of the different sample proportions you calculated in question 7b?

9. Now, examine Sample 1, which was computed using systematic sampling.

a. Does this sample meet the requirements of the Central Limit Theorem for approximation by the normal distribution? List each requirement, and whether it is met by this sample.

b. Now, using the mean and standard error for the sampling distribution you found in question 8, calculate the probability of finding a value as far from the mean as the sample proportion from Sample 1. (Hint: if , calculate ; if , calculate )

c. Does this result make sense, given the sample size and the population parameters you calculated?

Part III - Analysis and Conclusion

For this section, you will use the statistics computed in Part II to draw conclusions about the data and sampling methods used.

14. For each data set, you computed the probability of observing a sample mean when selecting a random sample from a population with known parameters.

a. The probability you computed in 9b represents the likelihood of selecting a sample with a similar proportion of repeat customers from the overall population. Assuming a probability of 5% or greater is reasonably likely, are you surprised by the observed results?

b. The probability you computed in 13 represents the likelihood of selecting a sample with a similar average customer rating from the overall population.

Assuming a probability of 5% or greater is reasonably likely, are you surprised by the observed results?

15. Suppose for the sample approval ratings in the approval.xlsx file, the sample was collected only from customers placing an order within the last month, while the population mean was computed using a customer history going back two years. What conclusions can you draw about customer approval ratings in the previous month compared to those in the past two years?